Response Surface Optimization Method for the Intake Air Duct of a Pendulum Mill

Abstract

A response surface optimization method for the intake air duct of a pendulum mill, belonging to the technical field of the design and optimization of pendulum mills. In order to solve the problem that the existing structural parameters of pendulum mills cannot well balance component wear and collection efficiency. The present invention models the main body of the pendulum mill, extracts the flow field model inside the main body, divides the grid and then imports it into the Fluent software for solution; for the pressure loss at the air duct outlet, one influencing factor is fixed respectively and any other two influencing factors are taken as variables to obtain the response surface of the influence on the pressure loss, so as to determine the pressure loss under the influence of each variable influencing factor and the significant influencing factors; for all influencing factors, they are processed in the same way as the pressure loss at the air duct outlet respectively to determine the candidate values of the influencing factors; according to the candidate values of the influencing factors, the eddy current situation of the wind field before and after optimization and the wear of the blades are analyzed, and finally the structural optimization result of the intake air duct of the pendulum mill is determined.

Description

Technical Field

[0001] The present invention belongs to the technical field of the design and optimization of pendulum mills, and relates to an optimization method for the intake air duct of a pendulum mill. Background Art

[0002] During the operation of a pendulum mill, the movement trajectory of material particles is affected by the forces from the flow field. The movement trajectory of material particles in the flow field can be divided into two stages: The first stage is that the material particles start from a stationary state and are gradually accelerated by the forces from the flow field; the second stage is that after the material particles reach a stable speed, they move uniformly along the direction of the flow field. In the first stage, the forces acting on the material particles mainly include gravity and drag force. Gravity causes the material particles to accelerate along the vertically downward direction, while the drag force hinders the falling of the material particles. When the speed of the material particles gradually increases, the drag force they receive gradually decreases until it balances with the gravity, and at this time, the material particles begin to enter the second stage.

[0003] In the second stage, the forces acting on the material particles in the flow field mainly include virtual mass force, pressure gradient force, Saffman lift force, Basset force, and Magnus lift force. The virtual mass force is the inertial force generated by the fluid motion on the material particles, which causes the material particles to accelerate along the direction of the flow field. The pressure gradient force is the force generated by the pressure change during the fluid motion, which causes the material particles to receive a force along the pressure gradient direction. The Saffman lift force is the lift force generated by the friction between the material particles and the fluid, which causes the material particles to deviate from the direction of the flow field. The Basset force is the force generated by the vortex shedding during the movement of the material particles in the flow field, which causes the material particles to receive a force deviating from the direction of the flow field. The Magnus lift force is the lift force generated by the rotation of the material particles, which causes the material particles to generate a moment deviating from the direction of the flow field in the flow field. In actual production, in order to improve the efficiency and stability of the transportation of material particles, it is necessary to optimize the action of these forces. On the one hand, the parameters of the flow field, such as flow velocity, flow direction, and fluid properties, can be adjusted to change the forces received by the material particles; on the other hand, the properties of the material particles, such as shape, size, and density, can be improved to reduce the influence of certain forces on the material particles.

[0004] Under the combined action of these forces, the movement trajectory of the material particles in the flow field becomes complex and diverse. In order to better master the movement law of the material particles, researchers have conducted in-depth studies on the action mechanism of these forces through methods such as experiments and numerical simulations. These research results have been widely applied in engineering practice, such as in the fields of powder transportation, particle separation, and fluidized bed reactors. After the material particles leave the scraper blade, they will be subject to gravity drag force virtual mass force pressure gradient force Saffman lift Basset force Magnus lift As shown in the following formula (1):

[0005]

[0006] In the formula, m p is the mass of the particle, kg; is the acceleration vector of the particle, m / s 2 .

[0007] The flow performance of solid particles in the flow field can be reflected by the Stocks number, that is, Stocks number = inertial force / resistance. The larger its value, the greater the inertial force or the smaller the resistance suffered by the particles, and the better the flow performance of the material particles. Its specific form is as follows

[0008]

[0009] In the formula, ρ p is the density of the material particles, kg / m 3 ; d p is the diameter of the material particles, m; u p is the velocity of the material particles in the flow field, m / s; u f is the flow field velocity, m / s; D is the diameter of the flow channel, m.

[0010] It can be seen from the above formula that the smaller the particle size, the more easily affected by the flow field. Considering the wear condition of the air duct component of the pendulum mill, when the wind field is uniform, the higher the wind speed, the fewer the number of particles passing through the guide vanes. However, too high a wind speed may lead to an increase in energy consumption or a phenomenon of coarse material running in the mill's collected material. The current structural parameters of the pendulum mill have the problem of not being able to well balance component wear and collection efficiency. Summary of the Invention

[0011] The present invention is to solve the problem that the current structural parameters of the pendulum mill cannot well balance component wear and collection efficiency.

[0012] A response surface optimization method for the intake air duct of a pendulum mill, comprising the following steps:[[]]

[0013] First, determine the simulation method and simulation process: For the main body of the pendulum mill, use 3D modeling software to model, extract the flow field model inside the main body, and use Fluent meshing to mesh the extracted flow field model; Import the obtained mesh file into the Fluent software, and perform solution in the Fluent software. During the solution process, perform simulation with particles of different particle size distributions distributed inside the main body, and perform Fluent-DEM coupled simulation calculation;

[0014] Based on the above-mentioned simulation method and process, determine the influencing factors to be optimized, including blade angle, number of blades, and volute line type. Take the influencing factors of the air duct as optimization parameters, and use the air duct outlet pressure loss, non-uniformity coefficient, main engine energy consumption, and air duct blade wear as objectives for simulation calculation: Use experimental design software to design experiments and statistically process the experimental results. For the air duct outlet pressure loss, fix one influencing factor and take any two other influencing factors as variables to obtain the response surface of the influence on the pressure loss, so as to determine the pressure loss and significant influencing factors under the influence of each variable influencing factor; Process the non-uniformity coefficient, main engine energy consumption, and air duct blade wear in the same way as the air duct outlet pressure loss; Determine the candidate values of the influencing factors based on the air duct outlet pressure loss, non-uniformity coefficient, main engine energy consumption, and air duct blade wear corresponding to different influencing factors.

[0015] Based on the above-mentioned simulation method and process, according to the candidate values of the influencing factors, analyze the eddy current situation of the air field before and after optimization and the wear of the blades, and finally determine the structural optimization result of the intake air duct of the pendulum mill.

[0016] Furthermore, during the process of meshing the extracted flow field model using Fluent meshing, the zonal meshing method is adopted for meshing. Dynamically partition the interior of the pendulum mill main engine to separate the rotating motion area from the stationary flow field area, and mesh the flow field inside the pendulum mill main engine.

[0017] Furthermore, when meshing the flow field inside the pendulum mill main engine, the global maximum size is set to 30 mm, and the mesh size in the rotating area is encrypted to a minimum of 1 mm.

[0018] Furthermore, during the process of solving in the Fluent software, the k-ε solution model is selected and the coupled algorithm is used for solving.

[0019] Furthermore, during the process of statistically processing the experimental results using experimental design software, the experimental design software used is Design-Expert version 13.

[0020] Furthermore, the number of blades in the finally determined structure of the intake air duct of the pendulum mill is 18.

[0021] Furthermore, the blade angle in the finally determined structure of the intake air duct of the pendulum mill is 55°.

[0022] Furthermore, the volute line type in the finally determined structure of the intake air duct of the pendulum mill is as follows:

[0023] The spiral line of the volute is drawn by the four-point unequal-distance square method; the volute is a four-segment arc structure, and the radii of the four arcs of the volute are 1870 mm, 1740 mm, 1600 mm, and 1450 mm respectively, and the arc radii are progressively reduced at intervals of 130 mm - 140 mm - 150 mm.

[0024] Beneficial effects:

[0025] The present invention determines the optimal structural parameters through response surface experimental design. The optimized wind field will help to adjust the particle trajectory, can improve the collection efficiency while reducing component wear, achieve a good balance between component wear and collection efficiency, and at the same time can reduce energy consumption. Description of the drawings

[0026] Figure 1 It is a design schematic diagram of different volutes.

[0027] Figure 2 It is a schematic diagram of the internal flow field grid division of the pendulum mill main machine.

[0028] Figure 3 It is a response surface diagram of the pressure loss.

[0029] Figure 4 It is a velocity contour map of the middle section of the air duct.

[0030] Figure 5 It is a velocity contour map of the main machine wind field trace.

[0031] Figure 6 It is a response surface diagram of the non-uniformity coefficient R.

[0032] Figure 7 It is a response surface diagram of the energy consumption.

[0033] Figure 8 It is a response surface diagram of the wear amount.

[0034] Figure 9 It is a particle distribution diagram at different blade angles.

[0035] Figure 10 It is a wear contour map of the guide vane and the corresponding enterprise wear-resistant patch map.

[0036] Figure 11 It is a velocity contour map of the wind field trace.

[0037] Figure 12 It is a turbulent kinetic energy contour map of the wind field trace.

[0038] Figure 13 It is a velocity contour map of the particle trace.

[0039] Figure 14 It is a particle size content curve graph before and after optimization. Detailed implementation mode Detailed implementation mode 1:

[0041] This implementation mode is a response surface optimization method for the air inlet duct of a pendulum mill, which determines the optimal structural parameters through response surface experimental design.

[0042] The Response Surface Methodology (RSM) is a multivariate data analysis technique widely used in fields such as engineering, manufacturing, bioscience, and finance. Through this method, the relationships between multiple input variables and output variables can be studied to find the optimal conditions, improve product performance, reduce costs, shorten the R & D cycle, etc. The core idea of the response surface optimization method is to establish a mathematical model between the input variables and output variables to study their relationships. Specifically, through experiments or simulations, data of input variables and output variables are obtained, and then these data are used to fit a mathematical model that can describe the relationship between the input variables and output variables.

[0043] Before specific description, first, one of the influencing factors to be optimized - the volute - is described:

[0044] The volute of the volute 1 is of a four-section type and is designed using the traditional structural square method. During design, according to the overall machine size, a square with a side length of 110 mm is constructed with the origin as the center. The four vertices of the square are the centers of the four-section arcs of the volute, and the arc radii are successively reduced by 110 mm at equal intervals. The four radii are 1880 mm, 1770 mm, 1660 mm, and 1550 mm respectively. Finally, the volute is manufactured through a welding process. This design method is simple to manufacture and convenient for subsequent processing. However, problems such as powder accumulation and blockage at the air duct inlet and volute wear occurred during on-site application, indicating insufficient wind energy at the volute tail. According to experience, the grinding mill manufacturing enterprise adopted a method of cutting a knife at the volute tail to improve the volute tail shrinkage, that is, the volute 1 (the existing volute structure of the enterprise), as shown in (a) of Figure 1 as shown in

[0045] Volute 2: The error between the spiral line drawn by the square method and the logarithmic spiral line is relatively large. In order to improve the performance of the centrifugal fan, at the same time, based on the CFturbo software design method, an attempt is made to draw the volute spiral line using the four-point unequal-spacing square method. The four-section arc radii of the volute 1 are adjusted. After multiple attempts and simulations, the four-section arc radii are 1870 mm, 1740 mm, 1600 mm, and 1450 mm respectively, and the arc radii are successively reduced in a progressive manner at intervals of 130 mm - 140 mm - 150 mm to obtain the volute 2, as shown in (b) of Figure 1 as shown in

[0046] Volute 3: CFturbo software is a structural design software specifically for pumps and fans. In the software, users can select different design modules according to their own needs to conduct various types of pump and fan designs. For example, the software provides a variety of impeller design tools, and users can select the appropriate impeller structure for design according to the uses and performance requirements of pumps and fans. In addition, the software also provides a powerful drawing function, and users can directly draw the structural diagrams of pumps and fans in the software and modify and optimize them, making the design more intuitive and efficient. Again, CFturbo software has a high degree of flexibility. It supports the input and output of multiple data formats and can be seamlessly docked with other relevant software, facilitating users to conduct data exchange and collaborative design. At the same time, the software also provides rich parameter setting and adjustment functions, and users can adjust various performance indicators of pumps and fans according to actual needs to meet different design requirements. In fact, subsequent designs and selection optimizations can be carried out for the volute line types of any other designs. In this embodiment, Figure 1 the volute line type shown in (c) in the middle is used as the volute 3 for description.

[0047] The main steps of the response surface optimization method of the present invention include:

[0048] (1) Experimental design: According to the principles of experimental design, select a set of input variables and their value ranges, and conduct experiments or numerical simulations.

[0049] (2) Fitting the response surface model: According to the experimental or numerical simulation data, establish a mathematical model to describe the relationship between the input variables and the output variables. Commonly used response surface models include polynomial regression models, neural network models, etc.

[0050] (3) Validating the model: Verify the effectiveness and reliability of the model by validating the prediction ability of the model.

[0051] (4) Optimization: Through the analysis of the response surface model and optimization algorithms, find the optimal solution to achieve the optimization of the output variables.

[0052] In order to further explore the distribution law of the main engine wind field, the blade angle, blade number, and volute line type of the air duct are used as optimization parameters, and the outlet pressure loss of the air duct, unevenness coefficient, main engine energy consumption, and air duct blade wear are used as objective functions. Referring to the reference parameter ranges given by the enterprise, the Box-Behnken response surface optimization method is used for experimental design. The experimental factor level table is shown in Table 1.

[0053] Table 1 Experimental factor level table

[0054]

[0055] Set the Fluent-DEM simulation parameters:

[0056] For the main body of the pendulum mill, model it in the 3D modeling software SpaceClaim. At the same time, utilize its powerful 3D modeling function to finely simplify the internal structure of the main body. During the simplification process, special attention should be paid to the detailed parts of the flow field, such as the rotating shovel blades, vanes, etc., to reflect the real flow field situation inside the main body to the greatest extent.

[0057] To ensure the accuracy of the internal flow field model, it is necessary to extract the flow field model inside the main body. Use Fluent meshing to perform mesh division on the extracted flow field model. To ensure the quality of mesh division, adopt zonal mesh division, dynamically partition the inside of the pendulum mill main body, separate the rotating motion area from the static flow field area, and perform mesh division on the flow field inside the pendulum mill main body. As Figure 2 shown. The purple area at the bottom represents a flow field area with the rotating motion of the shovel blades, while the meshes in the remaining parts represent the static flow field area. To ensure that the internal flow field environment can be accurately simulated in the simulation, the meshes in the shovel blade area are encrypted. The structure of the shovel blade area is relatively complex and there are many small characteristic structures. Therefore, the global maximum size is set to 30 mm during mesh division, and the mesh size in the rotating area is encrypted to a minimum of 1 mm.

[0058] Import the mesh file and set the boundary conditions: Import the mesh file obtained in the previous step into the Fluent software. In the Fluent software, set according to the performance parameters provided by the enterprise during the normal operation of the main body as shown in Table 2. On this basis, select a suitable k-ε solution model and use the coupled algorithm for solution.

[0059] Table 2 Main body flow field simulation parameters

[0060]

[0061] In the airflow field inside the main body, the interaction between gaseous and solid particles forms the coupling phenomenon of gas-solid two-phase flow. To simulate the wear condition of the air duct vanes, first set reasonable boundary conditions in the DEM discrete element software. Set the rotation speed of the shovel blade to 82 rev / min; the material density to 2700 kg / m3; the material feeding rate to 15 t / h; set the material parameters, etc.

[0062] Perform simulation on the particles with different particle size distributions inside the main body, as shown in Table 3. Through the Fluent-DEM coupled simulation calculation, detailed information about the internal flow field of the main body and the interaction between each phase can be obtained.

[0063] Table 3 Particle size distribution

[0064]

[0065] Response surface analysis: Through simulation experiments, the simulation results of each group were sorted out and are shown in Table 4. Among them, reducing pressure loss is an important evaluation index in mill production. The ventilation pressure loss of the mill and the pressure loss at each key part reflect the magnitude of the system air volume and the internal wind speed of the mill. Under the condition of unchanged structure, a large pressure loss indicates a large wind speed and a large air volume; a small pressure loss corresponds to a small wind speed and a small air volume. Maintaining a stable pressure loss reflects the stability of the wind speed and air volume, and further ensures the stability of the material layer. The unevenness coefficient at the outlet of the blade air duct reflects the uniformity of the intake air duct introducing into the main machine and changing the wind speed, and is also an important measurement index for the stability of the finished product collection air field inside the main machine. During the use of many pendulum mills, due to design or operation reasons, serious component wear often occurs. How to reduce wear and improve the service life of the equipment is an issue that pendulum mill operators and managers need to pay attention to.

[0066] Table 4 Statistical table of experimental design and results

[0067]

[0068] The test results were statistically processed using the experimental design (DOE) software Design-Expert version 13. In addition, to verify the validity of the data, a quadratic polynomial regression model was used for corresponding statistical verification. The fitted regression equations for the pressure loss P at the air duct outlet, the unevenness coefficient R, the main machine energy consumption M, and the blade wear D are as follows:

[0069] P = 403.91 + 26.09A + 14.36B - 101.62C + 18.62AB - 0.8875AC - 1.26BC + 20.06A 2 + 4.37B 2 + 162.51C 2

[0070] R = 0.3040 - 0.0663A - 0.0238B - 0.08C - 0.0050AB + 0.0175AC + 0.0125BC - 0.052A 2 - 0.0070B 2 - 0.0045C 2

[0071] M = 0.8540 + 0.0163A + 0.010B - 0.0763C + 0.015AB - 0.0025AC + 0.00BC - 0.0733A 2 - 0.0808B 2 + 0.0318C 2

[0072] D = 0.0001 + 0.0001A + 0.00B + 4.30E-06C + 3.150E-06AB + 5.625E-06AC + 5.250E-07BC + 0.00A 2 -2.795E-06B 2 + 0.00C 2

[0073] Among them, A, B, and C represent the blade angle, the number of blades, and the volute line type factor respectively.

[0074] Table 5 Analysis of variance table

[0075]

[0076] ※ indicates that the factor has a significant impact on the experimental index (Pr < 0.05)

[0077] The analysis of variance of the pressure loss and the non-uniformity coefficient is shown in Table 5. Among them, the lack-of-fit term is used to represent the fitting degree of the model to the experiment. The lack-of-fit value is greater than 0.05, indicating that there is no lack-of-fit factor in the model and the Pr value of the model < 0.05, indicating that the experimental design result has high reliability and the model can fit well with the actual value. It can be seen from Table 5 that the factors affecting the pressure loss from high to low are the volute line type > the blade angle > the number of blades. The blade angle and the volute line type have a significant impact on the pressure loss (P < 0.05). Increasing the blade angle and improving the volute line type are both beneficial to improving the air flow uniformity inside the pendulum mill. The factors affecting the non-uniformity coefficient at the air duct outlet from high to low are the volute line type > the blade angle > the number of blades, and they are all significant influencing factors (P < 0.05). Among them, changing the blade angle, the number of blades, and the volute line type are all beneficial to improving the air flow uniformity inside the pendulum machine.

[0078] The response surface of each factor to the pressure loss is shown in Figure 3 , Figure 3Among them, (a) is the response surface of AB factors, (b) is the response surface of BC factors, and (c) is the response surface diagram of AC factors. When the volute line type remains unchanged, as the blade angle and the number of blades increase, the pressure loss at the air duct outlet also increases. When the blade angle is 55° and the number of blades is 20, the pressure loss reaches the maximum value of 498.86 Pa. When the number of blades remains unchanged, as the blade angle increases and the volute line type is poor, the pressure loss at the air duct outlet also increases; when the blade angle is 55° and the volute line type is 1, the pressure loss reaches the maximum value of 701.94 Pa. When the blade angle remains unchanged, as the number of blades increases and the volute line type is poor, the pressure loss at the air duct outlet also increases. When the number of blades is 20 and the volute line type is 1, the pressure loss reaches the maximum value of 689.7 Pa. The influence of the volute line type on the pressure loss is the most significant. As the volute line type is improved, the pressure loss decreases significantly. Appropriately increasing the blade angle and improving the volute line type are both beneficial to improving the air flow uniformity inside the pendulum machine and reducing the pressure loss. At the same time, too many blades will lead to an increase in the pressure loss.

[0079] Figure 4 is the velocity contour map of the middle section of the air duct. Among them, (a) is the original model and (b) is the optimized model diagram. According to the statistical results of the response surface experimental design, it is obtained that the pressure loss at the air duct outlet of the combination of blade angle 55°, number of blades 18, and volute 1 is the largest, which is 701.94 Pa. The velocity contour map of the middle section of the air duct of this combination is as Figure 4 shown in (a) of the figure. Due to the unreasonable volute line type, the velocity distribution of the volute air duct is uneven. The velocity at the front end of the volute near the air inlet is large and relatively concentrated. At the same time, since the 55° blade angle significantly increases the wind speed compared with the 50° blade angle, and there is a positive correlation between the wind speed and the pressure loss, resulting in a large air duct pressure loss. The pressure loss at the air duct outlet of the combination of blade angle 50°, number of blades 18, and volute 2 is the smallest, which is 380.94 Pa. After the volute line type of this combination is optimized, the velocity distribution of the volute air duct is uniform, which can effectively reduce the pressure loss. At the same time, due to the unreasonable 50° blade angle, there are large areas of vortices between the blades as Figure 4 shown in (b) of the figure. It is verified that the volute line type is a significant factor affecting the pressure loss.

[0080] Figure 5 is the velocity contour map of the main engine wind field trace. Among them, (a) is the original model and (b) is the optimized model diagram. The velocity contour map of the main engine wind field trace of the combination of blade angle 55°, number of blades 18, and volute 1 is as Figure 5As shown in (a). The air entering from the inlet passes through the guide of the volute and the blades and enters the main machine. Driven by the scraper, the air shows a spiral upward trend inside the hood. It can be intuitively found that the local wind speed in the volute part of this group is too high, which increases the pressure loss, and the air fails to enter the main machine evenly, effectively and in a timely manner. In contrast, the wind field trace distribution of the main machine with a blade angle of 50°, 18 blades, and volute 2 is more uniform as Figure 5 in (b). The air entering from the inlet can be evenly sent into the main machine by the optimized volute, which can improve the air volume utilization rate and thus improve the grinding efficiency. Secondly, the optimized volute reduces the wind resistance and energy consumption.

[0081] The response surfaces of various factors on the non-uniformity coefficient of the air duct outlet are as Figure 6 shown, where (a) is the response surface of factors A and B, (b) is the response surface of factors A and C, and (c) is the response surface of factors B and C. When the volute line type remains unchanged, as the blade angle and the number of blades continuously decrease, the non-uniformity coefficient continuously increases. When the blade angle is 46° and the number of blades is 16, the non-uniformity coefficient reaches the maximum value of 0.33. When the number of blades remains unchanged, as the blade angle continuously decreases and the volute line type is poor, the non-uniformity coefficient continuously increases. When the blade angle is 45° and the volute line type is 1, the non-uniformity coefficient reaches the maximum value of 0.42. When the blade angle remains unchanged, as the number of blades continuously decreases and the volute line type is poor, the non-uniformity coefficient continuously increases. When the number of blades is 16 and the volute line type is 1, the non-uniformity coefficient reaches the maximum value of 0.41. The influence of the volute line type on the non-uniformity coefficient R of the air duct outlet is the most significant, followed by the blade angle and the number of blades. Appropriately adjusting the blade angle, increasing the number of blades, and selecting a suitable volute line type can reduce the non-uniformity coefficient R of the air duct outlet, thereby improving the air flow uniformity inside the pendulum mill.

[0082] Table 6 Analysis of variance table

[0083]

[0084] ※ indicates that the factor has a significant impact on the experimental index (Pr < 0.05)

[0085] The analysis of variance of the main machine energy consumption and blade wear is shown in Table 6. It can be seen from the table that the factors affecting the unit energy consumption of the main machine from high to low are volute line type > blade angle > number of blades. The blade angle and volute line type have a significant impact on the energy consumption (Pr < 0.05). Reducing the blade angle and improving the volute line type are both beneficial to reducing the energy consumption inside the pendulum mill. The factors affecting blade wear from high to low are blade angle > number of blades > volute line type. The blade angle and number of blades have a significant impact on wear (Pr < 0.05). Among them, reducing the blade angle and the number of blades is beneficial to reducing the wear amount of the blades.

[0086] The response surfaces of various factors on the main engine energy consumption are as Figure 7 shown. Among them, (a) is the response surface of factors A and B, (b) is the response surface of factors A and C, and (c) is the response surface of factors B and C. When the volute profile remains unchanged, with the continuous increase of the blade angle and the number of blades, the unit energy consumption of the main engine first increases and then decreases. When the blade angle is 51° and the number of blades is 18, the unit energy consumption of the main engine reaches the maximum value of 0.87 kJ / kg. When the number of blades remains unchanged, with the continuous increase of the blade angle and the optimization of the volute profile, the unit energy consumption of the main engine shows a downward trend. When the blade angle is 51° and the volute profile is 1, the unit energy consumption reaches the maximum value of 0.94 kJ / kg. When the blade angle remains unchanged, with the continuous increase of the number of blades and the optimization of the volute profile, the unit energy consumption of the main engine shows a downward trend. When the number of blades is 18 and the volute profile is 1, the unit energy consumption reaches the maximum value of 0.93 kJ / kg. As can be seen from Table 6, the volute profile has the most significant influence on the main engine energy consumption. It can be seen from the figure that with the improvement of the volute profile, the main engine energy consumption decreases significantly. Appropriately increasing the blade angle and improving the volute profile are both beneficial to improving the air flow uniformity inside the pendulum machine and reducing the energy consumption.

[0087] The response surfaces of various factors on the blade wear are as Figure 8 shown. Among them, (a) is the response surface of factors A and B, (b) is the response surface of factors A and C, and (c) is the response surface of factors B and C. When the volute profile remains unchanged, with the continuous increase of the blade angle and the number of blades, the blade wear amount continuously increases. When the blade angle is 55° and the number of blades is 20, the wear amount reaches the maximum value of 1.84E - 04 m. When the number of blades remains unchanged, with the continuous increase of the blade angle and the optimization of the volute profile, the blade wear amount continuously increases. When the blade angle is 55° and the volute profile is 3, the wear amount reaches the maximum value of 2.06E - 04 m. When the blade angle remains unchanged, with the continuous increase of the number of blades and the optimization of the volute profile, the blade wear amount continuously increases. When the number of blades is 20 and the volute profile is 3, the wear amount reaches the maximum value of 1.13E - 04 m. The blade angle has the most significant influence on the blade wear. It can be seen from the figure that with the decrease of the blade angle, the blade wear decreases significantly. Appropriately reducing the blade angle and the number of blades are both beneficial to reducing the blade wear amount and improving the service life of the components.

[0088] In the pendulum mill, the guide vane introduces the wind field into the main engine, guiding the movement of materials and improving the pulverization and collection efficiency. However, if the angle of the guide vane is not reasonably designed, it will lead to the existence of eddy currents in the wind field, a large number of particles between the blades, and serious wear. When the angle of the guide vane is set to 50° as Figure 9As shown in (a), the angle design of the blades is unreasonable, there are many vortices in the flow field between the blades, and the uniformity is poor. The material keeps rotating between the blades, increasing the number of frictions and collisions between the particles and the blades, resulting in serious wear. When the blade angle is optimized to 55°, as shown in Figure 9 (b), after the flow field is optimized, the vortices between the blades are reduced and the flow field is smoother, thus reducing the particles between the blades and reducing the wear. This is of great significance for improving the operating stability of the equipment and extending the service life of the blades. At the same time, due to the reduced wear, the maintenance cost of the equipment is also correspondingly reduced, thus reducing the overall operating cost of the enterprise.

[0089] To reduce the wear of the guide vanes, the first thing that comes to mind is to adjust the angle of the blades. Through research, it is found that adjusting the angle of the guide vanes to 55° can reduce the wear between the blades to a certain extent. It should also be noted that the problem of wear still exists at the position where the inner side of the 55° guide vane is in direct contact with the particles. After many tests and studies, the above adjustment cannot well solve the wear problem and will also affect other factors. Therefore, the method of using wear-resistant patches is adopted to solve the wear problem. Figure 10 For the wear cloud map of the guide vane and the corresponding enterprise's wear-resistant patch, the enterprise decides to install a wear-resistant patch on the inner side of the guide vane as shown in the right physical diagram in Figure 10 The wear-resistant patch is a composite material with high wear resistance. Installing it on the guide vane can effectively improve the wear resistance of the blade and extend the service life. After this method is implemented, remarkable results have been achieved. It not only solves the problem of serious wear on the inner side of the guide vane, but also reduces the maintenance cost of the enterprise and improves the production efficiency.

[0090] Under the premise of minimizing the pressure loss and non-uniformity coefficient through response surface analysis, multi-objective optimization based on the response surface is carried out to obtain the optimal combination data of the volute and blade structures. The optimal scheme is volute 2, the number of blades is 18, and the blade angle is 55°. The following is a comparative study of the enterprise's existing mill scheme (volute 1, blade angle 50°, number of blades 18) and the optimized scheme. Combining the DPM multiphase flow analysis technology in Fluent, the whole machine is simulated, and the collection efficiency of 200-mesh (75μm) finished particles is studied. Among them, the collection efficiency of the pendulum mill has an important impact on its competitiveness in the field of ultrafine powder production. The level of this index directly reflects the competitive strength of the pendulum mill in the industry. The collection efficiency M can be calculated according to formula (3):

[0091]

[0092] In the formula, N e is the mass flow rate of the finished particles collected at the outlet, kg / s; N iis the total fine particle mass flow rate at the inlet, in kg / s. Specifically, the collection efficiency can be the ratio of the mass of the finished particles collected by the mill from the crushed fine particles to the total fine particle mass.

[0093] Figure 11 is the contour map of the whole-machine wind field trace line velocity. Among them, (a) is the original model, and (b) is the optimized model diagram. The contour map of the wind field trace line velocity of the original model shows a relatively chaotic distribution. The wind field flow is not stable enough, and there are large-scale vortices, increasing the energy consumption, as Figure 11 (a), while after optimization, that is Figure 11 (b), the wind field trace line contour map becomes more orderly and stable. Under the action of the blade diversion, the wind flows inward along the air duct. The rotational movement of the roller scraper will form a vortex in the middle area of the main machine. The wind field of the main air duct rotates upward along the inner wall surface of the hood barrel, and the uniform flow field significantly improves the vortex phenomenon and reduces the energy consumption.

[0094] Figure 12 is the contour map of the turbulent kinetic energy of the whole-machine wind field trace line. Among them, (a) is the original model, and (b) is the optimized model diagram. In the original model, the local turbulent kinetic energy in the blade area and the classifier classification area is relatively large, and there are obvious vortex areas and uneven distributions, resulting in a significant reduction in the air flow velocity, such as Figure 12 (a). In the model after structural optimization, such as Figure 12 (b), the turbulent kinetic energy between the blades is small, and the vortex area has been significantly improved. The concentrated area of turbulence in the classifier classification area is reduced, and the wind field is evenly distributed, thus reducing the vortex. The stable wind field is conducive to the transportation of particles, and finally achieves the purpose of reducing energy consumption and improving the collection efficiency.

[0095] Figure 13 is the particle trace line contour map. Among them, (a) is the original model, and (b) is the optimized model diagram. The particle trace line velocity contour map shows the movement trajectory and velocity of the particles in the wind field. In the original model Figure 13 (a), the uneven wind field causes the trajectories of some particles to be relatively concentrated and chaotic and irregular when approaching the classifier. This unstable movement trajectory leads to a reduction in the collection efficiency, making it impossible to effectively capture and transport the particles. In the optimized model Figure 13 (b), the wind field has been significantly improved and is more evenly distributed. This uniform wind field makes the movement of the particles orderly and stable, which is conducive to the particles accurately reaching the classifier position.

[0096] Further organize the simulation results. The total machine pressure loss of the original model is 2808.53 Pa, and the outlet wind speed is 33.7 m / s. The total machine pressure loss of the optimized model is 2836.34 Pa, and the outlet wind speed is 32.93 m / s. According to the pressure loss ΔP (Pa) formula: ΔP = K * ρ * V 2 / 2; where K is the resistance coefficient; ρ is the air density, kg / m³; V is the wind speed, m / s. There is a positive correlation between the wind speed and the pressure loss. After optimization, the angle of the air duct blades of the model is 55°, which increases the wind speed entering the main machine. The flow rate of the air flow in the main machine speeds up, and at the same time, the resistance in the blade area increases, resulting in a greater pressure loss. Given that the overall height of the machine is 4.9 m, calculated by formula 2-4, the unit mass energy consumption of the original model and the optimized scheme are 1.98 kJ / kg and 2.03 kJ / kg respectively. Due to the change in the blade angle in the two schemes, there is a change in the resistance coefficient of the intake air duct. Therefore, the energy consumption of the optimized scheme increases slightly. Calculated by formula 2-5, the power consumption of the original model and the optimized scheme for the whole machine are 37.6 kW·h and 38.55 kW·h respectively. Further calculation of the collection efficiency shows that the collection efficiency of the finished product (particles within 200 meshes) of the original model is 84%, while the collection efficiency of the optimized model increases to 95.3%, which is 13.4% higher than the original model. That is, under the same order of magnitude of equipment energy consumption, the production capacity of the equipment has increased significantly, and the optimization effect is obvious.

[0097] Production tests were carried out on the optimized mill, and limestone was selected as the raw material. And a BT-9300T laser particle size analyzer was used to conduct particle size analysis and comparison of the products. The particle size content curve is as Figure 14 shown, and the cumulative collection efficiency is shown in Table 7. Comparing the collection efficiency of the 200-mesh product, the original design of the enterprise was 89.36%, which was highly consistent with the simulation analysis. The optimized version of the mill was 95.30%. Therefore, the reliability of this data is relatively high. The optimized scheme can obtain smaller and finer powder sizes, and the product quality is more stable.

[0098] Table 7 Cumulative collection efficiency

[0099]

[0100] The present invention uses Fluent simulation technology and response surface optimization technology to conduct response surface experimental analysis on the optimized design of the intake air duct of the pendulum mill, and studies the pressure loss at the air duct outlet, the uneven coefficient at the air duct blade outlet, energy consumption, blade wear and finished product collection efficiency. Among them, the process of blade wear is studied in detail through the coupling of Fluent and DEM, and the characteristics and mechanisms of blade wear under different working conditions are explored, providing a theoretical basis for optimizing blade design and improving its service life. The following conclusions are drawn:

[0101] (1) The influence laws of blade angle, blade number, and volute line type on the pressure loss at the air duct outlet, the non-uniformity coefficient of the air duct, the main engine energy consumption, and blade wear are studied using the Box-Behnken response surface design method. The response surface analysis results show that for the pressure loss at the air duct outlet, both the blade angle and the volute line type are significant factors, while the blade number factor is not significant; for the non-uniformity coefficient at the air duct outlet, all three factors are significant, and the volute line type is the most significant; for the main engine energy consumption, both the blade angle and the volute line type are significant factors, with the volute line type being the most significant, and the blade number factor is not significant; for blade wear, both the blade angle and the blade number are significant factors, and the volute line type is not significant; appropriately adjusting the blade angle and optimizing the volute structure can effectively improve the ventilation performance of the mill and increase production efficiency. Considering the manufacturing cost, the optimal solution is determined to be 18 blades, a blade angle of 55°, and volute 2.

[0102] (2) To verify the effectiveness of the optimized design, by comparing the original model of the whole machine with the optimized scheme, the finished product collection efficiency of the original model is 84%, while the finished product collection efficiency of the optimized model is increased to 95.3%, which is 13.4% higher than that of the original model. The overall pressure loss of the original model is 2808.53 Pa, and the overall pressure loss of the optimized model is 2836.34 Pa, showing a slight increase compared to the original model, but negligible compared to the increase in the finished product collection efficiency. This result indicates that the optimized design and simulation analysis can achieve the air flow field regulation and verification simulation of the mill, and at the same time proves the potential of the research method in improving the production efficiency of the pendulum mill, providing a feasible solution for the equipment optimization in the industrial powder making field.

[0103] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations should all fall within the protection scope of the appended claims of the present invention.

Claims

1. A response surface optimization method for the air intake duct of a pendulum mill, characterized in that: The steps include the following: First, determine the simulation method and process: For the main body of the pendulum mill, use 3D modeling software to model, extract the flow field model inside the main body, and use Fluent meshing to mesh the extracted flow field model; import the obtained mesh file into Fluent software, and perform calculations in Fluent software. During the calculation process, simulate with particles of different particle size distributions inside the main body, and perform Fluent-DEM coupled simulation calculations; Based on the above simulation method and process, determine the influencing factors to be optimized, including blade angle, number of blades, and volute line type. Take the influencing factors of the air duct as optimization parameters, and use the air duct outlet pressure loss, unevenness coefficient, main body energy consumption, and air duct blade wear as targets for simulation calculations: Use experimental design software to design experiments and statistically process the experimental results. For the air duct outlet pressure loss, fix one influencing factor and use any two other influencing factors as variables to obtain the response surface of the influence on the pressure loss, so as to determine the pressure loss under the influence of each variable influencing factor and the significant influencing factors; process the unevenness coefficient, main body energy consumption, and air duct blade wear in the same way as the air duct outlet pressure loss; Based on the air duct outlet pressure loss, unevenness coefficient, main body energy consumption, and air duct blade wear corresponding to different influencing factors, determine the candidate values of the influencing factors; Based on the above simulation method and process, according to the candidate values of the influencing factors, analyze the air flow eddy situation before and after optimization and the wear of the blades, and finally determine the structural optimization result of the intake air duct of the pendulum mill.

2. The response surface optimization method for the air inlet duct of a pendulum mill according to claim 1, characterized in that: During the process of using Fluent meshing to mesh the extracted flow field model, use the partitioned mesh method for meshing, dynamically partition the inside of the main body of the pendulum mill, separate the rotating motion area from the stationary flow field area, and mesh the flow field inside the main body of the pendulum mill.

3. The response surface optimization method for the air inlet duct of a pendulum mill according to claim 2, characterized in that: When meshing the flow field inside the main body of the pendulum mill, the global maximum size is set to 30 mm, and the mesh size in the rotating area is encrypted to a minimum of 1 mm.

4. The response surface optimization method of the intake air duct of a pendulum mill according to claim 1, characterized in that: During the process of performing calculations in Fluent software, select the k-ε calculation model and use the coupled algorithm for calculation.

5. The response surface optimization method of the air inlet duct of a pendulum mill according to claim 1, characterized in that: During the process of statistically processing the experimental results using experimental design software, the experimental design software used is Design-Expert version 13.

6. A response surface optimization method for the intake air duct of a pendulum mill according to any one of claims 1 to 5, characterized in that: The number of blades in the finally determined structure of the intake air duct of the pendulum mill is 18.

7. A response surface optimization method for the intake air duct of a pendulum mill according to claim 6, characterized in that: The blade angle in the finally determined structure of the intake air duct of the pendulum mill is 55°.

8. The response surface optimization method for the intake air duct of a pendulum mill according to claim 7, characterized in that: The volute line type in the finally determined structure of the intake air duct of the pendulum mill is as follows: Use the four-point unequal-distance square method to draw the volute spiral line; the volute is a four-section arc structure, and the radii of the four arcs of the volute are 1870 mm, 1740 mm, 1600 mm, and 1450 mm respectively, and the arc radii gradually decrease in a progressive manner with a spacing of 130 mm - 140 mm - 150 mm.

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